Research Papers

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A Juzvinskiĭ Addition Theorem for Finitely Generated Free Group Actions
with Yonatan Gutman

arXiv
Harmonic models and spanning forests of residually finite groups
with Hanfeng Li

arXiv
On a co-induction question of Kechris
with Robin Tucker-Drob
to appear in Israel J. of Math.
arXiv
Random walks on coset spaces with applications to Furstenberg entropy


arXiv
Pointwise ergodic theorems beyond amenable groups
with Amos Nevo to appear in Ergodic Theory and Dynam. Systems arXiv
Geometric covering arguments and ergodic theorems for free groups
with Amos Nevo
arXiv
Every countably infinite group is almost Ornstein

to appear in Contemporary Mathematics.
arXiv
Sofic entropy and amenable groups

to appear in Ergodic Theory and Dynam. Systems arXiv
Stable orbit equivalence of Bernoulli shifts over free groups

Groups Geom. Dyn. 5 (2011), no. 1, 17–38. arXiv
Orbit equivalence, coinduced actions and free products

Groups Geom. Dyn. 5 (2011), no. 1, 1–15. arXiv
Entropy for expansive algebraic actions of residually finite groups

Ergodic Theory Dynam. Systems. 31 (2011), no. 3, 703--718. arXiv
Weak isomorphisms between Bernoulli shifts

Israel J. of Math, (2011) Volume 183, Number 1, 93-102
arXiv
Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula

Ergodic Theory Dynam. Systems 30 (2010), no. 6, 1629--1663. arXiv
The ergodic theory of free group actions: entropy and the f-invariant.

Groups Geom. Dyn. 4 (2010), no. 3, 419--432 arXiv
A new measure conjugacy invariant for actions of free groups

Ann. of Math., vol. 171 (2010), No. 2, 1387--1400. arXiv
Measure conjugacy invariants for actions of countable sofic groups

J. Amer. Math. Soc., 23 (2010), 217-245. arXiv
Invariant measures on the space of horofunctions of a word hyperbolic group

Ergodic Theory Dynam. Systems. 30 (2010), no. 1, 97--129. arXiv
Free groups in lattices

Geometry & Topology, 13, (2009), 3021--3054. arXiv
A generalization of the prime geodesic theorem to counting conjugacy classes of free subgroups

Geom. Dedicata, 124, (2007), 37--67. arXiv
A Solidification Phenomenon in Random Packings
with Russell Lyons, Charles Radin and Peter Winkler SIAM J. Math. Anal. 38 (2006), no. 4, 1075--1089.
Fluid/Solid Transition in a Hard-Core System
with Russell Lyons, Charles Radin and Peter Winkler Phys. Rev. Lett. 96, 025701 (2006)
Uniqueness and symmetry in problems of optimally dense packings
with Charles Holton, Charles Radin and Lorenzo Sadun Math. Phys. Electron. J. 11 (2005), Paper 1, 34 pp. arXiv
On the Gromov Norm of the Product of Two Surfaces
with Mike Develin, Jesus De Loera and Francisco Santos Topology 44 (2005), no. 2, 321--339. erratum: Topology 47 (2008), no. 6, 471--472. arXiv
Couplings of Uniform Spanning Forests

Proc. Amer. Math. Soc. 132 (2004), no. 7, 2151--2158. arXiv
Optimally Dense Packings of Hyperbolic Space
with Charles Radin Geom. Dedicata 104 (2004), 37--59. arXiv
On the existence of completely saturated packings and completely reduced coverings

Geom. Dedicata 98 (2003), 211--226. arXiv
Densest Packing of Equal Spheres in Hyperbolic Space
with Charles Radin
Discrete Comput. Geom. 29 (2003), no. 1, 23--39. 
Periodicity and Circle Packing in the Hyperbolic Plane

Geom. Dedicata 102 (2003), 213--236. arXiv
Circle Packing in Hyperbolic Space

Math. Phys. Electron. J. 6 (2000), Paper 6, 10 pp. (electronic).


This material is based upon work supported by the National Science Foundation under Grants No. 0901835 (9/1/09-2/28/10), 0968762 (9/1/09-8/31/12) and 0954606 (5/15/10-4/30/15). The collaborative work with Amos Nevo was supported by the Binational Science Foundation under Grant No. 2008274 (9/1/09-8/31/13).

Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the Binational Science Foundation.